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11.3. Positron Emitters
Table of Contents
Positron emission
Positron emitters are radionuclides that decay by emitting a positron, the antiparticle of the electron. In GATE you do not manually script every emitted positron. Instead, you typically select a radionuclide, such as F‑18 or Ga‑68, and let the radioactive decay physics model generate the entire decay chain, including the positron and any accompanying gamma rays.
At the nuclear level, a typical positron emission is a beta plus decay. A proton in the nucleus transforms into a neutron, a positron, and a neutrino. Energy released in this process appears as kinetic energy of the emitted particles. In practice, the positron energy is not a single value but follows a continuous beta spectrum that starts at zero and ends at the maximum endpoint energy characteristic of that radionuclide. For example, F‑18 has a relatively low endpoint energy, while some other radionuclides used in research can have significantly higher endpoint energies.
In a GATE simulation, when you choose a given PET radionuclide, the energy spectrum of emitted positrons is automatically handled by the Geant4 radioactive decay models. This is important, because the initial energy distribution of the positrons strongly influences how far they travel in tissue, how much energy they deposit locally, and how precisely the annihilation location represents the original emission site.
When configuring positron emitters in GATE, two concepts are especially relevant. First, the activity distribution, which determines how many decays occur per unit time and where they occur in space. Second, the isotope choice, which sets the positron energy spectrum and anti coincidence gamma emissions. By combining an appropriate activity distribution with the correct radionuclide, you can create realistic sources for PET scanner simulations, internal dosimetry, or other applications where positron transport and annihilation matter.
For a positron-emitting radionuclide, the emitted positron energy follows a continuous beta spectrum from $0$ up to a radionuclide-specific endpoint energy. This spectrum directly affects positron range and PET spatial resolution.
Positron range
Once emitted, a positron travels through matter while losing energy through interactions with electrons and nuclei. It undergoes many small-angle scatterings and ionizations until its kinetic energy becomes very low. Only then can it annihilate with an electron. The path it follows is not straight, and the total distance traveled along its curved track, called the track length, is larger than the net displacement between the emission point and the annihilation point. For PET, we are usually interested in the net displacement in tissue, often referred to as the positron range.
The positron range depends mainly on three factors, the initial positron energy, the composition and density of the surrounding medium, and the detailed physics models that describe positron transport. Higher-energy positrons can travel further before annihilating, so radionuclides with higher endpoint energies produce a larger average range. In water-like tissue, a typical F‑18 positron travels only a fraction of a millimeter on average before annihilation, whereas positrons from higher-energy isotopes can travel several millimeters.
In GATE, you do not assign a fixed range. Instead, you select an appropriate physics list that includes detailed electromagnetic processes for electrons and positrons. The Geant4 transport engine then simulates ionization, multiple scattering, and other relevant processes step by step until the positron slows down and annihilates. This microscopic simulation naturally produces a realistic distribution of annihilation positions around the emission site, which can be analyzed using actors that record annihilation coordinates or deposited energy.
The positron range introduces an intrinsic blurring in PET images. Even if your scanner had perfect spatial resolution, the annihilation photons would not come exactly from the original emission point. The amount of blurring depends on the radionuclide and the surrounding medium. When you design PET simulations in GATE, it is therefore important to select a physics configuration that correctly models positron interactions, particularly for high-energy positron emitters or for simulations that aim to evaluate spatial resolution limits.
Positron range in tissue increases with positron energy. Higher endpoint energy radionuclides cause larger average annihilation displacements, which degrade intrinsic PET spatial resolution.
Annihilation photons
When a positron has lost most of its kinetic energy, it encounters an electron and the particle–antiparticle pair annihilates. In matter at rest, the most probable outcome is the emission of two photons, each with energy approximately $511 \,\text{keV}$, moving in nearly opposite directions to conserve energy and momentum. These annihilation photons are the fundamental signal detected in PET.
In reality, the two photons are not exactly back-to-back, and they may not have exactly equal energies if the electron or positron still has residual momentum. This leads to a small angular deviation from perfect collinearity and tiny energy shifts relative to the ideal $511 \,\text{keV}$. In GATE, both the residual motion of the annihilating particles and the detailed gamma interaction physics are modeled according to the chosen physics list. As a result, the directions and energies of the annihilation photons in the simulation reflect realistic physical distributions rather than idealized values.
After creation, the annihilation photons travel through the surrounding medium and may undergo photoelectric absorption, Compton scattering, or pair production if their energy and the local material allow it. In PET energy ranges, Compton scattering is particularly important. It changes the photon energy and direction before detection, and this can lead to scattered coincidences where the detected line of response is no longer aligned with the true annihilation site.
In a GATE-based PET simulation, annihilation photons are not treated differently from any other gamma rays. They are transported according to the selected electromagnetic physics, can interact multiple times, and may or may not reach the detector. To study annihilation photon behavior, you can use actors to record gamma tracks, energy deposition in detector crystals, or coincidence data after digitization. These tools allow you to investigate how annihilation photon interactions, scattering, and absorption influence image quality, scatter fraction, and sensitivity.
Positron annihilation typically produces two photons of approximately $511 \,\text{keV}$ that are almost but not perfectly back-to-back. Their subsequent interactions, especially Compton scattering, strongly affect PET image quality and scatter fractions.
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